Guess That Sequence! is a game that can develop skills with finding patterns and understanding sequences and functions. The game is played in the following way: one student (call her Student S) in a group of three or more begins the game by announcing that she has come up with a sequence. Student S then says the first three elements of the sequence and asks the other students if they have any guesses for what rule she is using. After all the other students have made their guesses or declined the opportunity, the Student S either says which students got the sequence she was thinking of, or if no one guessed correctly, lists the next three elements of the sequence.
Play continues until one of the students correctly guesses the sequence or the number of revealed elements of the sequence reaches a certain predefined upper limit. The game can be played with or without this upper limit but its presence is recommended as it can be used to encourage stronger students to come up with sequences that are within the realm of capability of their weaker peers.
The first student(s) to correctly guess the sequence receive two points. If no students correctly guess the sequence before the upper limit has been reached, nobody gets a point.
The student activity sheet we include is geared toward high school students after their first exposure to geometric series, but Guess That Sequence! is an adaptable game and can be used with students of any age. Elementary school children, for instance, could make patterns using markers and paper and ask each other to guess the pattern. The fundamental goal of Guess That Sequence! is to help students learn to identify patterns; but beyond that, it can be used to give students practice with concepts (for instance, recursively defined functions) that they encounter in class.
